SOLUTION: Express in terms of i. - sqrt -50 i got -4i*sqrt 10. is this correct?

Question 665620: Express in terms of i.
- sqrt -50
i got -4i*sqrt 10. is this correct?

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Nope, close but no cigar.
Use the (very powerful) identity
(1) sqrt(a*b) = sqrt(a)*sqrt(b)
Apply this to sqrt(-50)
First we have
(2) sqrt(-50) = sqrt(-1)*sqrt(50), OK so far?
Using i to represent the imaginary factor sqrt(-1), we get
(3) sqrt(-50) = i*sqrt(50)
Now apply (1) to get
(4) sqrt(50) = sqrt(25)*sqrt(2) or
(5) sqrt(50) = 5*sqrt(2)
Put (5) into (3) to yield
(6) sqrt(-50) = (5i)sqrt(2) or
(7) -sqrt(-50) = -5i*sqrt(2)
Answer: -sqrt(-50) is given by (7)
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